"It just continues to sound like they are getting closer and closer," Kiffin said. "It could be today, you just never know. I know that the sides are as close as they've ever been."
Russell's agents and reps from the Raiders have been in sporadic contact for the past several weeks before negotiations picked up in the last few days. Monday marked the third straight day the two sides met.
Asked if he expected Russell to be signed in time for the Raiders' trip to Denver on Sunday, Kiffin was hesitant but optimistic.
"I wouldn't say I expect that," Kiffin said, "but I definitely wouldn't be surprised."
When a deal is struck, it would end the longest contract holdout by a Raiders draft pick in the modern era and put a new spin on Oakland's quarterback situation.
Though he's highly unlikely to be ready to play for the first two months of the season, the pressure to play Russell in a game will mount if the team isn't winning.
Josh McCown started in Sunday's 36-21 loss to Detroit and put up impressive numbers, completing 30 of 40 attempts for 313 yards and two touchdowns. He was also intercepted twice and fumbled three times.
Kiffin reiterated Monday that McCown will remain the Raiders starter for Oakland's game against the Broncos.